David Cameron's declaration of war on "gang culture" after the 2011 riots is branded a failure in a report that says the police's focus on arresting gang leaders while failing to act against other members has backfired.

The study also accuses ministers of "losing commitment" to the fight, allowing more and more primary schoolchildren to be drawn into gangs, with some now wearing gang "colours" to lessons. The report by the Centre for Social Justice, an independent thinktank established by the work and pensions secretary, Iain Duncan Smith, and obtained by the Observer in advance of publication on Monday, cites professionals as saying the arrests by police of about 200 gang leaders since the riots have led to more violence rather than less.

The CSJ says this is because the arrests have caused vacuums, in which more volatile gang members compete for power – and that arresting leaders has not been followed by action against the junior gang members who remain.

It also cites frontline organisations and charities as reporting an increase in the number of girls being recruited into gangs and an increase in intra-gang sexual violence, as organisers seek to spread their influence. Entitled Time to Wake Up:Tackling Gangs One Year After the Riots, the report is particularly explosive because Duncan Smith is one of the cabinet ministers charged with spearheading government responses to the riots.

After the riots, Cameron said there would be an "all-out war on gangs and gang culture", led by the home secretary, Theresa May, and Duncan Smith. "It is a major criminal disease that has infected streets and estates across our country," he said. Policy initiatives on prevention, punishment and support were announced.

May said in November 2011 that "gang and youth violence is not a problem that can be solved by enforcement alone. We need to change the life stories of young people currently ending up dead or wounded on our streets or locked in a cycle of reoffending."

However, the CSJ says: "Many in Whitehall regard the riots as a random one-off, and mistake the quashing of the disorder as control of the streets. They could not be more wrong. The alarming fact is that many streets across the country are besieged by anarchy and violence. There is no control in such neighbourhoods."

Christian Guy, managing director of the CSJ, says: "Gangs played a significant role in the riots and it is dangerous to pretend otherwise. In London at least one in five of those convicted was part of a gang."

The report says people it spoke to on the frontline reported a "marked increase in the violent behaviour of some gangs. The removal of 'elders' [leaders] by the police was cited as integral to this development; preceding elders were described as having a 'code' in which certain acts – such as shooting a rival gang member when accompanied by his mother – were understood to be unacceptable and not committed.

"There was a consensus that the current gangs neither have such a code nor cohesive leadership, which is resulting in increased chaos, violence and anarchy."

The Home Office, although presented with the main findings of the report, said it could not comment in detail on a study it had not seen in full. But a spokesman reiterated the series of announcements made by ministers last year. These included establishing an Ending Gang and Youth Violence Team and the allocation of £10m of Home Office funding for this year and next to support up to 30 local areas to help "identify, assess and work with the young people most at risk of serious violence".

The CSJ report recommends a number of approaches, including: "working with children and young people already involved in gangs, but also addressing the drivers of gang culture, not just the symptoms. The surest way of eliminating gangs is to try to ensure that children and young people never want or feel the need to join them. To do this we need to tackle deeper issues in our society and seek to nurture and support ever strong families and stronger communities."

The CSJ's views are echoed by Junior Smart, an ex-offender and former London gang member, who is leading a major project in south London that works to wean young people off crime and violence. "People take sides. If one gang or another territorial street network knows that an elder has been taken out, then they suddenly think that gang is weak, 'We can take them'. And so we have inter-estate disputes going on."

A Home Office spokesman said: "There are no quick fixes, but we are seeing results. The Crime Survey for England and Wales shows that crime is down by 6%, and police figures show knife crime is down by 9%."

The Metropolitan police said that since Trident Gang Crime Command was set up in February as a dedicated unit to tackle gang crime, the results had been impressive. By September overall serious youth violence was down by 34%, equating to 1,000 fewer victims.